Linearized Optimization for Enhanced Aggregate Modeling of Invisible Hybrid Distributed Energy Resources

Abstract

The increasing penetration of distributed energy resources (DERs)—including photovoltaics, wind turbines, and battery energy storage systems—poses challenges for modern power distribution systems, particularly in scenarios with high penetration of DERs outside the monitoring capabilities of distribution utilities. Addressing invisible DERs in operational planning studies requires innovative modeling methodologies, often involving aggregated models. This paper proposes a mixed-integer linear programming (MILP) formulation to locate and size aggregate hybrid DER models in radial distribution systems by minimizing residuals in the estimates of existing field measurements. These equivalent models grasp the collective effect of many invisible DERs and enable the reconstruction of unobserved bus voltages and branch flows, enhancing system visibility. Case studies demonstrate average errors below 5% for the estimation of unobserved branch flows with limited voltage magnitude measurements. OpenDSS is employed to showcase the computational efficiency and accuracy of the proposed method, also under unbalanced system loading conditions.